Measuring Variation Patterns of distribution

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Measuring Variation Patterns of distribution

• Normal distributions
• Most common type to describe individuals w/in
  populations
• Bell shaped
• More are closer to the average than to the
  extremes
• Based on continuous variables
•  
• Binomial distributions
• Good for gene/allele distributions w/in a
  population
• Uniform and predictable,
• Binomial (polynomial) equations, (pq)2
• Pascals triangle used to calculate coefficients
• Based on discrete variables
• Poisson distributions
• Few populations, good for spatial or temporal
  patterns in ecology
• Usually Skewed, not uniform
• More are close to one extreme than the other
• Based on discrete variables indiv. in area
•  

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Measuring Variation Descriptive Statistics of a
Population

• Central Tendencies of data in a population
• Mean, Avg. ( x )
• Calculated value as the average of observations
• Continuous variables or counts
• Ex. Body wt.(g) 125, 134, 139, 142, 147, 147,
  156, x 141.4g
• Median, M,
• used for averages of ranked data, (percentiles,
  quartiles)
• the middle value, if odd
• Ex. Body wt.(g) 125, 134, 139, 142, 147, 147,
  156, M 142g
• the average of two central values, if even
• Ex. Body wt.(g) 125, 134, 139, 142, 147, 156,
  M 140.5g
• Mode
• Observed value that most frequently occurs
• Ex. Body wt.(g) 125, 134, 139, 142, 147, 147,
  156 147g

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Measuring Variation Descriptive Statistics of a
Population

• Distribution of data in a population
• Range, observed dispersion of data
• max and min values
• Variance, s2
• estimates the width of dispersion of a measurable
  parameter in a population about its mean ( x )
• Normal or bell shaped distributions
• Mean, median, mode are equal

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Measuring VariationDescriptive Statistics of a
Population

• Degree of Variation of a measurable parameter
• Standard deviation, s or sd
• Sq. root of Variance, ?s2
• 1 sd unit the mean 68 pop.
• 2 sd units the mean 95 pop.
• ( 1.96 sd units min. for significance)
• 3 sd units the mean 99 pop

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Measuring VariationWhisker-Box Plot
Comparisons can be visualized using a whisker-box
plot. Often means separated by at least 2 sd
units are likely to be significantly different
and should be subjected to statistical testing.
Range whisker
Mean whisker
sd box 1 sd
Dependent variable
1 sd
Species 1
Species 2
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Measuring VariationDescriptive Statistics of a
Population

• Comparing means for significance using a
  whiskers-box plot.
• Means are expected to be significantly different
  because they are separated by more than 2 sd.

1 sd
1 sd
1 sd
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Measuring VariationDescriptive Statistics of a
Population

• Comparing means for significance using a
  whiskers-box plot.
• Means are NOT significantly different because
  they are separated by less than 2 sd.

1 sd
1 sd